arXiv subjects

Liang Jiang

Publications and source records attributed to Liang Jiang.

At least 19 recordsLinked to original sources

arXiv2026

A generative foundation model for computational brain imaging

Computational brain imaging is constrained by a mismatch between increasingly diverse tasks and scarce, heterogeneous clinical data. Although existing brain foundation models transfer pretrained representations, their knowledge remains entangled within model-specific features and fixed architectures. This paper proposes BrainGFM, a generative foundation model that extends knowledge transfer beyond representation reuse through a reusable and reconfigurable brain-imaging prior. By pretraining on a corpus of about 1.3 million MRI and CT slices, BrainGFM supported task-aligned data synthesis for low-data predictive learning and task-adapted post-training for image reconstruction. Across 48 downstream tasks, BrainGFM improved segmentation and classification under limited supervision and achieved high-fidelity image enhancement across heterogeneous imaging conditions. Multicenter clinical validation involving 4,796 stroke patients across two internal and four external centers demonstrated its applicability to three clinically relevant tasks around stroke cohorts. Blinded reader assessments showed that BrainGFM-generated FLAIR images approached acquired FLAIR in overall diagnostic quality. In a human-AI collaboration study, BrainGFM assistance yielded a 14% relative improvement in mean radiologist stroke-subtyping accuracy. These findings support generative priors as a reusable foundation for heterogeneous computational brain-imaging applications.

cs.AI↗

arXiv2026

Supervised Learning with Quantum Hamiltonian Embeddings

Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.

quant-ph↗

arXiv2026

Learning Midcircuit Measurement Backaction from Three Repeated Measurements

Accurate modeling of midcircuit measurements (MCMs) is essential for dynamic-circuit operations such as syndrome extraction, measurement-based reset, and the separation of state-preparation and measurement error. Unlike terminal measurement, a noisy MCM both produces a classical outcome and alters the incoming quantum state, thereby influencing subsequent circuit operations. This makes conventional confusion-matrix or fidelity-level characterization insufficient. Here, we introduce an efficient, self-consistent protocol for learning a single-qubit Z-twirled MCM instrument, retaining the readout-backaction correlations and excitation-decay asymmetry that are erased in Pauli-error descriptions. Remarkably, readout bit strings from only three repeated MCMs on a maximally mixed input determine all learnable parameters of the reduced instrument, up to a single unidentifiable gauge degree of freedom. Physicality constraints convert this nonidentifiability into narrow, gauge-aware error intervals. Implemented on IBM superconducting processors, the learned instrument improves Pauli-observable prediction by $\sim 100\times$ over a conventional confusion-matrix model and reveals a $T_1$-decay dominated backaction. Our protocol provides a compact characterization layer for state-preparation and measurement error separation, reset optimization, and noise-aware quantum error correction.

quant-ph↗

arXiv2026

Logical computation with canonical lifted product codes

High-rate quantum low-density parity-check (qLDPC) codes encode many logical qubits with low physical-qubit overhead, but realizing efficient fault-tolerant computation on such dense encodings remains a major challenge. Generic, code-agnostic techniques such as code surgery and gate teleportation apply broadly, but are difficult to make modular, low-overhead, and fully certifiable on complex high-rate codes whose structure is left unexploited. Here we overcome these obstacles by co-designing the code together with its logical instruction set for a broad family of canonical lifted-product (LP) codes with cyclic symmetry. We show that these codes admit a canonical logical basis, in which conjugate logical operators are organized into rows and columns of cyclic orbits inherited directly from the underlying classical codes, analogous to the structure that makes hypergraph-product codes so tractable. This canonical basis enables universal logical processing using magic-state input and a constant number of reusable seed surgery gadgets---only two (resp. four) for a $[[1122,148,\leq 20]]$ (resp. $[[4350,1224,\leq 20]]$) LP code. A fixed extractor smaller than half the data block also enables arbitrarily high-weight logical Pauli-product measurements (PPMs) while preserving the code's cyclic symmetry. These codes also enable rigorously fault-tolerant parallel logic, including PPMs across all logical qubits and magic-state injection from many surface codes into a full LP block. For example, a $[[468,36,20]]$ (resp. $[[952,112,17]]$) code supports simultaneous measurements of arbitrary logically disjoint Pauli products with an ancilla overhead of roughly three (resp. four) times the data block size. These results advance the frontier of fault-tolerant quantum computation on ultra-high-rate quantum architectures.

quant-ph↗

arXiv2026

Scaling Quantum Networks via Phase-Stable Vacuum Beam Guide: Architectural Blueprint and Benchmark

Scaling quantum networks to continental distances requires physical infrastructure capable of overcoming both exponential attenuation and severe phase decoherence. While the concept of the vacuum beam guide (VBG) has recently emerged as a promising low-loss solution, we move beyond it by proposing a stringent and conservative physical-layer architectural blueprint anchored by empirical data and methods from Advanced LIGO, particularly regarding its interferometric stability in dynamic environments. To evaluate its system-level viability, we benchmark this architecture against various protocols across quantum communication, metrology, and computation. Ultimately, we identify no fundamental technical blockers to scaling this infrastructure.

quant-ph↗

arXiv2026

Doing More with Less Tokens: Hierarchical Reinforcement Learning for Efficient Coding Agents

Recently, coding agents have emerged as a dominant paradigm for real-world software engineering (SWE) scenarios, which solve complex tasks through multi-turn interactions with development environments. However, frequent interactions with environments would inevitably introduce substantial token overhead, leading to high usage costs and latency. Although recent studies have explored reducing token usage by context manipulation and interaction limits at inference time, these approaches focus on improving token efficiency while overlooking the risk of discarding task-relevant information, thus struggling to balance the trade-off between resolution rate and token efficiency. In this paper, we study a more general paradigm without suffering from the limitation, i.e., training token-efficient coding agents with promising resolution performance, which is a highly-practical yet less-explored problem. To this end, we reveal two core observations in SWE scenarios: i) Efficiency Variation: successful resolution could be achieved with fewer tokens; ii) Entropy Correlation: unproductive behaviors are associated with turn-level entropy. Motivated by observations, we propose a novel reinforcement learning framework, dubbed HERO. Specifically, HERO prioritizes task resolution over token efficiency during policy optimization and encourages efficient reasoning patterns at both trajectory and turn levels. Extensive experiments on SWE-bench Verified and SWE-bench Multilingual demonstrate that HERO achieves a favorable trade-off between resolution rate and token efficiency compared with state-of-the-art coding agents and reinforcement learning methods.

cs.SE↗

arXiv2026

Generalized Reimpell-Werner Iteration

Quantum measurements and channels determine how information is extracted, encoded, and transmitted in quantum protocols. Optimizing their performance often requires numerical methods that remain practical as Hilbert space dimensions increase. The Reimpell-Werner iteration offers a practical approach to these tasks through repeated matrix updates that respect the constraints. Here, we generalize this iteration to linear objectives with arbitrary Hermitian cost matrices. We prove that the iterates converge to a global optimum whenever the initialization satisfies suitable support overlap conditions. For each fixed problem, choice of iteration parameters, and admissible initialization, $\mathcal{O}(1/\varepsilon)$ iterations suffice asymptotically to bring the objective value within $\varepsilon$ of the optimum. These results provide a rigorous foundation for the iteration and broaden the class of optimization problems to which its convergence guarantees apply.

quant-ph↗

arXiv2026

Optimal two-mode bosonic loss codes from finite group symmetry

Photon loss is a dominant noise process in bosonic quantum hardware, including superconducting cavities. Fixed-total-photon-number qubit encodings in two bosonic modes retain the loss-detection advantage of dual-rail qubits while supporting photon loss correction. Optimizing entanglement fidelity in this setting for $4\leq n\leq25$ over arbitrary encoders and decoders reveals finite-group structure in every best-found code: 11 correspond to two-dimensional irreducible representations and 11 to reducible ones. Motivated by this emergence, we derive the necessary-and-sufficient Knill-Laflamme conditions for arbitrary finite-group-invariant codes, reducing their construction to equations on representation multiplicity spaces. For every finite subgroup of $SU(2)$ and every tensor rank, we explicitly construct the minimum number of operators required to impose all corresponding loss-correction constraints. These results produce analytic counterparts to most numerical codes and predict constructions missed by the initial search. Exact MacWilliams-Farkas certificates show that our codes achieve the maximum possible loss distance in 21 of the 22 sectors, and we prove that the resulting distance bound is monotone in total photon number. Beyond the scan, we identify a binary-polyhedral sequence with photon number $n_d=\lceil(3d^2+1)/4\rceil$ and construct each corresponding code through distance $d=10$. To our knowledge, the constructed $(n,d)=(28,6),(49,8),(76,10)$ codes give the smallest reported $n$ for their respective distances; all members through $d=9$ attain the fixed-$n$ LP distance bound. Together, these constructions, certificates, and a symmetry-reduced constraint count provide evidence for an infinite code family conjectured to attain every distance at the minimum photon number.

quant-ph↗

arXiv2026

Active-SWE: Benchmarking Coding Agents for Proactive Bug Fixing without Issue Reports

Coding agents powered by large language models (LLMs) are increasingly adopted in software engineering (SWE) scenarios, capable of fixing a specific bug in large-scale codebase. However, existing SWE benchmarks typically assume that high-quality issue reports with detailed information are always available, which is easily violated in practice due to the complexity of report acquisition and curation. To address this, we introduce Active-SWE, a benchmark for evaluating coding agents on proactively discovering and fixing multiple bugs without report guidance, covering 1,663 tasks across six bug categories and eight languages. Beyond shifting the focus from existing reactive bug fixing to proactive bug fixing, Active-SWE enables a more in-depth evaluation by expanding the scope from fixing a specific recorded bug to multiple-bug fixing and potential bug discovery scenarios. To construct Active-SWE, we propose a novel difficulty-aware task formulation pipeline with a dual-track evaluation framework, facilitating comprehensive evaluation of proactive bug-fixing capability. Extensive experiments reveal that most state-of-the-art coding agents struggle with proactive bug-fixing tasks, demonstrating limited performance in locating and resolving recorded bugs, handling multiple bug fixing scenarios, and discovering valid potential bugs.

cs.SE↗

arXiv2026

Learning sparse quantum states from single-qubit measurements

We study the problem of learning a sparse quantum state, an $n$-qubit quantum state whose density matrix has at most $s$ nonzero matrix entries in an unknown product basis. While such states admit compact classical descriptions, they can carry long-range entanglement that prevents reconstruction from local reduced density matrices alone. Therefore, previous learning approaches addressed such long-range-entangled states using many entangling gates to extract the necessary information. In this work, we show that sparse states can nevertheless be efficiently learned using only single-qubit measurements. Specifically, when the sparsity $s$ is constant, our algorithm can learn sparse states from single-qubit measurements with polynomial sample complexity and classical computational complexity. When $s$ grows polynomially with $n$, sparse states can still be learned from single-qubit measurements with polynomial sample complexity, although efficient classical computation is not guaranteed in general. In this regime, however, the classical computational complexity becomes quasipolynomial when the state is sparse in an unknown basis that is a product of a known fixed finite set of single-qubit bases (e.g., eigenbases of Pauli operators). These results establish efficient learning of sparse states with long-range entanglement without entangling gates, and the single-qubit measurement requirements make our algorithms compatible with current quantum devices.

quant-ph↗

arXiv2026

Quantum channel learning with limited parallel access

Quantum channels can be characterized by their action on an orthogonal operator basis, where these operators are related to observable properties of the quantum system. For qudit and multimode bosonic systems, this is encoded respectively in the Heisenberg--Weyl transfer matrix estimated from the Choi-state, and in the characteristic-function transfer map estimated from a two-mode squeezed vacuum based Choi-state. We derive sample-complexity bounds for estimating entries of the transfer matrix/map to additive accuracy $ε$ with success probability $\ge1-δ$, under different resources: access to the complex-conjugate channel $\mathcal{E}^*$ and/or parallel access to $c$ copies. In all settings, the learner uses parallel channel calls with adaptively chosen, ancilla-assisted input states and measurements. Absolute values of transfer-matrix entries can be learned efficiently with simultaneous access to $\mathcal{E}$ and $\mathcal{E}^*$, with tight scaling $ε^{-4}$. Without conjugate access, any $c<d$ copies are insufficient for efficient learning, requiring sample complexity exponential in the number of ($d$-level) qudits $n$ (for prime $d$). Efficiency is recovered at $c=d$, with tight scaling $ε^{-2d}$. For bosonic systems, exponential sample complexity holds in terms of an effective dimension induced by an energy constraint for all $c=O(1/ε)$. Although the task is learning a particular state, these bounds carry stronger implications than standard state-learning bounds since the learner controls the inputs and has ancillary assistance. This establishes a hierarchy of channel-learning resources: self-complex-conjugate channels require two-copy ancilla-assisted access for efficient learning, while for every square-free $d$, some channels require $d$-copy access. As a corollary, we derive tighter lower bounds for state learning with limited multi-copy access.

quant-ph↗

arXiv2026

Hybrid Device Design for a Pump-Free Microwave-Optical Bell-Pair Source

Hybrid quantum devices offer a route to combine complementary functionalities of disparate physical systems within a single architecture. Extending this concept to a three-way interface among optical, microwave, and single-spin degrees of freedom is particularly challenging because of the weak magnetic interaction between an individual spin and a microwave photon. Here, we propose a hybrid device architecture that integrates a single diamond color center with a superconducting parallel-plate microwave resonator and a photonic-crystal cavity. The parallel-plate geometry drastically reduces the resonator impedance and enhances the single-spin microwave coupling rate by an order of magnitude. The enhanced interaction allows the optical cavity to be spatially separated from the superconducting structure while retaining appreciable microwave coupling and optical cooperativity above 1. For both NV$^-$ and ${}^{117}$SnV$^-$ centers, numerical simulations predict microwave coupling rates in the kilohertz range together with optical cooperativity exceeding 1. This architecture provides a promising route toward single-spin microwave-optical hybrid quantum devices enabling functionalities such as pump-free microwave-optical Bell-pair generation.

quant-ph↗

arXiv2026

Pump-Free Microwave-Optical Bell Pair Generation for Teleportation-Based Quantum Transduction

The coherent conversion between microwave and optical photons, known as quantum transduction, is critical for connecting superconducting processors to optical networks. Existing methods are limited by complications associated with optical pumping. We propose a pump-free microwave-optical Bell-pair source for teleportation-based transduction. Using a spin or atomic system resonantly coupled to optical and microwave cavities, the scheme generates loss-robust heralded Bell pairs. Across color centers, atomic ensembles, and phonon-mediated systems, this assembly achieves kilohertz-range heralding rates with high fidelity.

quant-ph↗

arXiv2026

Optimal Hamiltonian Parameter Estimation in the Presence of Nuisance Parameters

In many sensing applications, the quantity of interest is not the only unknown, there are also additional unknown parameters, known as nuisance parameters, that affect the precision of estimation. While the ultimate local precision limit for a target parameter is well understood in the absence of nuisance parameters, the problem becomes significantly more challenging when they are present. In this work, we develop a framework for optimal Hamiltonian parameter estimation in the presence of nuisance parameters. We introduce an effective generator that captures the influence of nuisance parameters on the target precision, providing an explicit characterization of the ultimate precision limit for estimating the target parameter. Finally, we provide explicit optimal protocols, including probe state, control, and measurement that saturate this fundamental limit.

quant-ph↗

arXiv2026

Global Precision Bounds and Success-Probability Guarantees in Quantum Parameter Learning

Quantum metrology offers the possibility of quantum enhancements of the precision of various sensing tasks. In this manuscript, we tackle two open problems in the theory of single-shot quantum parameter learning, going beyond the usual setting of local parameter estimation via repeated measurements. The first concerns the construction of global upper bounds on the learning precision. The second concerns rigorous guarantees on the success probability of parameter learning, namely, lower bounds on the probability of learning a parameter with a certain precision, given the constraints on the resources used for the quantum metrology task. We provide rigorous, practical, and global upper bounds and success-probability guarantees for quantum parameter learning. Most importantly, we establish a fidelity-based learning guarantee for generic mixed-state models that can be viewed as the achievability-side analogue of the quantum Cramer-Rao bound. Whereas the latter provides a no-go constraint, based on the local curvature of the fidelities, our bound uses only pairwise fidelities between parameter-encoded states to certify that a prescribed precision is attainable with a guaranteed success probability. We demonstrate the versatility of the new bounds in a Rabi-frequency-learning example involving a driven qubit coupled to a bosonic environment and a collective-spin Hamiltonian learning problem. Together, the new global bounds and success-probability guarantees allow us to rule out unattainable precision and to certify attainable precision beyond what is possible via standard Fisher-information analysis or binary hypothesis testing bounds. They also allow one to tractably characterize the performance of various learning schemes, without the overhead of an explicit simulation.

quant-ph↗

arXiv2026

Efficient Entanglement Purification Circuit Design for Dual-Species Atom Arrays

Entanglement purification protocols (EPPs) are essential for generating high-fidelity entangled states in noisy quantum systems, enabling robust quantum networking and computation. Building on the circuit of the foundational recurrence protocol, we generalize two-way EPPs to arbitrary stabilizer codes. Through analytical derivations and noisy circuit simulations incorporating circuit-level noise, we demonstrate enhanced purification performance, with fidelity improvements and finite distillation rates for distillable input states. We propose efficient circuit designs for EPPs tailored to dual-species Rydberg atom arrays, leveraging species-specific laser control and interspecies Rydberg interactions. Introducing a low-overhead operation set, the dual-species atom convenient operation set, we facilitate straightforward compilation of EPP circuits without the need for ancillary atoms or complex atom rearrangements. Our framework provides practical guidance for near-term implementations on dual-species platforms, advancing towards scalable entanglement distribution in neutral atom systems and paving the way for fault-tolerant quantum technologies.

quant-ph↗

arXiv2026

High-Rank Encoding Can Improve Approximate Quantum Error Correction

Conventional quantum-code constructions encode pure logical states as pure code states, but this restriction can sacrifice performance. We show that intrinsic encoding randomness can improve optimal entanglement fidelity. We bound the loss from imposing a rank-one encoder and prove it is at most quadratic near perfect recovery after joint optimization. The optimized advantage survives small noise perturbations. An explicit noise family requires higher-rank encoders arbitrarily close to perfect recovery, with every optimal encoder mapping pure inputs to mixed code states.

quant-ph↗

arXiv2026

Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order

Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this work, we exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a single non-Abelian anyon type. Furthermore, we use Bayesian inference to obtain a statistical mechanics model for fixed-point non-Abelian TOs with perfect measurements under any noise model, which yields the optimal threshold conditioned on measuring anyon syndromes. We numerically illustrate these results for $D_4 \cong \mathbb Z_4 \rtimes \mathbb Z_2$ TO. In particular, for non-Abelian charge noise and perfect syndrome measurement, we find a conditioned optimal threshold $p_c=0.218(1)$, whereas an intrinsically heralded minimal-weight perfect-matching (MWPM) decoder already gives $p_c=0.20842(2)$, outperforming standard MWPM with $p_c = 0.15860(1)$. Our work highlights how non-Abelian properties can enhance stability, rather than reduce it, and discusses potential generalizations for achieving fault tolerance.

quant-ph↗